when i kill somthing in arena a chain link shows up with a number what does it mean

the longer the chain is, the more exp and better chance of getting good drops for you

The Monster Chain Counter (also known as the MCC) appears when fighting monsters in the Arena. If you click Resummon monster within a few seconds of killing the previous monster you summoned, the chain should appear, and start counting for each additional kill you make. If you take too long between resummons, use a fish, or leave the arena, you will lose your MCC. Additionally, if you level or are not fighting monsters of the same level as you, the MCC will not appear. This means that you cannot get the MCC above level 70.

While the MCC is present, you get a bonus to experience and item drops corresponding to the number displayed on the MCC. The higher it gets, the more bonus you will receive.

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